Factoring when a = 1

Front

What is factoring in algebra?

Back

Factoring is the process of breaking down an expression into simpler components, or factors, that when multiplied together give the original expression.

Front

What does it mean when a = 1 in factoring?

Back

When a = 1, the quadratic expression is in the form x² + bx + c, making it easier to factor by finding two numbers that multiply to c and add to b.

Front

Factor the expression: x² + 11x + 24

Back

(x + 8)(x + 3)

Front

Factor the expression: x² - 15x + 50

Back

(x - 10)(x - 5)

Front

Factor the expression: d² - 10d + 25

Back

(d - 5)(d - 5)

Tags

CCSS.HSA.APR.C.4

Front

Factor the expression: x² + 12x + 35

Back

(x + 5)(x + 7)

Front

Factor the expression: r² - 16r + 60

Back

(r - 6)(r - 10)

Front

What are the steps to factor a quadratic expression?

Back

1. Identify a, b, and c from ax² + bx + c. 2. Find two numbers that multiply to ac and add to b. 3. Rewrite the expression using these numbers. 4. Factor by grouping.

Front

What is a prime polynomial?

Back

A prime polynomial is a polynomial that cannot be factored into simpler polynomials with integer coefficients.

Front

What is the significance of the discriminant in factoring?

Back

The discriminant (b² - 4ac) helps determine the nature of the roots of a quadratic equation. If it's positive, there are two distinct real roots; if zero, one real root; if negative, no real roots.

Tags

CCSS.HSA-REI.B.4B